Question

Y= (2x(x+3)) / (x-1)the x intercept is supposedly -0.5 how do I get this answer?​

a) Solve for x when y = 0
b) Substitute x = -0.5 into the equation
c) Set the numerator equal to zero
d) Divide by x-1

Answer 1

To find the x-intercept of the function y = (2x(x+3)) / (x-1), set y to 0 and determine the values of x for which the numerator (2x(x+3)) is equal to 0. The correct x-intercepts are found to be x = 0 and x = -3, not x = -0.5.

Step-by-step explanation:

To find the x-intercept of the equation y = (2x(x+3)) / (x-1), you can follow these steps:

1. Set y to 0 because at the x-intercept, the value of y is always 0.
2. Rewrite the equation as 0 = (2x(x+3)) / (x-1).
3. Since the equation is in the form of a rational expression, the x-intercept occurs when the numerator is equal to 0, ignoring the denominator as long as x is not equal to 1 (which would cause the denominator to be 0).
4. Set the numerator equal to 0: 2x(x+3) = 0.
5. Solve for x by factoring: 2x = 0 or x+3 = 0, giving us two solutions: x = 0 and x = -3.

In conclusion, the x-intercepts are x = 0 and x = -3, not x = -0.5 as the student initially supposed.